395 research outputs found
Voluntary Societies and Urban Elites in 19th Century Italy
Paper given at European History [E-seminars
Recent Results on the Periodic Lorentz Gas
The Drude-Lorentz model for the motion of electrons in a solid is a classical
model in statistical mechanics, where electrons are represented as point
particles bouncing on a fixed system of obstacles (the atoms in the solid).
Under some appropriate scaling assumption -- known as the Boltzmann-Grad
scaling by analogy with the kinetic theory of rarefied gases -- this system can
be described in some limit by a linear Boltzmann equation, assuming that the
configuration of obstacles is random [G. Gallavotti, [Phys. Rev. (2) vol. 185
(1969), 308]). The case of a periodic configuration of obstacles (like atoms in
a crystal) leads to a completely different limiting dynamics. These lecture
notes review several results on this problem obtained in the past decade as
joint work with J. Bourgain, E. Caglioti and B. Wennberg.Comment: 62 pages. Course at the conference "Topics in PDEs and applications
2008" held in Granada, April 7-11 2008; figure 13 and a misprint in Theorem
4.6 corrected in the new versio
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Complex systems approach to language games
The mechanisms leading language conventions to be socially accepted and adopted by a group are object of an intense debate. The issue can be of course addressed by different points of view, and recently also complex system science has started to contribute, mainly by means of computer simulations and analytical approaches. In this paper we study a very simple multi-agent model of convention spreading and investigate some of the crucial aspects of its dynamics, resorting, whenever possible, to quantitative analytic methods. In particular, the model is able to account for the emergence of global consensus out of local (pairwise) interactions. In this regard, a key question concerns the role of the size of the population. We investigate in detail how the cognitive efforts of the agents in terms of memory and the convergence time scale with the number of agents. We also point out the existence of an hidden timescale ruling a fundamental aspect of the dynamics, and we discuss the nature of the convergence process
2-D constrained Navier-Stokes equation and intermediate asymptotics
We introduce a modified version of the two-dimensional Navier-Stokes
equation, preserving energy and momentum of inertia, which is motivated by the
occurrence of different dissipation time scales and related to the gradient
flow structure of the 2-D Navier-Stokes equation. The hope is to understand
intermediate asymptotics. The analysis we present here is purely formal. A
rigorous study of this equation will be done in a forthcoming paper
Self-Structuring of Granular Media under Internal Avalanches
We study the phenomenon of internal avalanching within the context of
recently proposed ``Tetris'' lattice models for granular media. We define a
recycling dynamics under which the system reaches a steady state which is
self-structured, i.e. it shows a complex interplay between textured internal
structures and critical avalanche behavior. Furthermore we develop a general
mean-field theory for this class of systems and discuss possible scenarios for
the breakdown of universality.Comment: 4 pages RevTex, 3 eps figures, revised version to appear in Phys.
Rev. Let
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Self-organizing communication in language games
From the point of view of semiotic dynamics language is an evolving complex dynamical system. In this perspective, unrevealing the mechanisms that allow for the birth of shared conventions is a major issue. Here we describe a very simple model in which agents negotiate conventions and reach a global agreement without any intervention from the outside. In particular we focus on the possibility of predicting on which of the several competing conventions the agreement is reached. We find from simulations that early created conventions are favored in the competition process and this advantage can be quantified. Beyond the specific results presented here, we think that this paper provides an example of a new way of investigating language features where simple models allow for the investigation of precise problems and, possibly, for analytical approaches
Coarsening and Slow-Dynamics in Granular Compaction
We address the problem of the microscopic reorganization of a granular medium
under a compaction process in the framework of Tetris-like models. We point out
the existence of regions of spatial organization which we call domains, and
study their time evolution. It turns out that after an initial transient, most
of the activity of the system is concentrated on the boundaries between
domains. One can then describe the compaction phenomenon as a coarsening
process for the domains, and a progressive reduction of domain boundaries. We
discuss the link between the coarsening process and the slow dynamics in the
framework of a model of active walkers on active substrates.Comment: Revtex 4 pages, 4 figures, in press in PRL. More info
http://axtnt3.phys.uniroma1.it/Tetri
Conformal approach to cylindrical DLA
We extend the conformal mapping approach elaborated for the radial Diffusion
Limited Aggregation model (DLA) to the cylindrical geometry. We introduce in
particular a complex function which allows to grow a cylindrical cluster using
as intermediate step a radial aggregate. The grown aggregate exhibits the same
self-affine features of the original cylindrical DLA. The specific choice of
the transformation allows us to study the relationship between the radial and
the cylindrical geometry. In particular the cylindrical aggregate can be seen
as a radial aggregate with particles of size increasing with the radius. On the
other hand the radial aggregate can be seen as a cylindrical aggregate with
particles of size decreasing with the height. This framework, which shifts the
point of view from the geometry to the size of the particles, can open the way
to more quantitative studies on the relationship between radial and cylindrical
DLA.Comment: 16 pages, 8 figure
Free-volume kinetic models of granular matter
We show that the main dynamical features of granular media can be understood
by means of simple models of fragile-glass forming liquid provided that gravity
alone is taken into account. In such lattice-gas models of cohesionless and
frictionless particles, the compaction and segregation phenomena appear as
purely non-equilibrium effects unrelated to the Boltzmann-Gibbs measure which
in this case is trivial. They provide a natural framework in which slow
relaxation phenomena in granular and glassy systems can be explained in terms
of a common microscopic mechanism given by a free-volume kinetic constraint.Comment: 4 pages, 6 figure
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